Let KG be a non-commutative group algebra of a torsion nilpotent group G over a field K of positive characteristic p whose unit group, (KG), is solvable. In the present note we prove that dl((KG)) ≥ ⌈log2(p 1)⌉ and characterize group algebras for which this lower bound is achieved. © de Gruyter 2010.
On the derived length of the unit group of a group algebra / Francesco, Catino; Spinelli, Ernesto. - In: JOURNAL OF GROUP THEORY. - ISSN 1433-5883. - STAMPA. - 13:4(2010), pp. 577-588. [10.1515/jgt.2010.008]
On the derived length of the unit group of a group algebra
SPINELLI, ERNESTO
2010
Abstract
Let KG be a non-commutative group algebra of a torsion nilpotent group G over a field K of positive characteristic p whose unit group, (KG), is solvable. In the present note we prove that dl((KG)) ≥ ⌈log2(p 1)⌉ and characterize group algebras for which this lower bound is achieved. © de Gruyter 2010.File allegati a questo prodotto
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